Definition 31.19.1. Let $f : Z \to X$ be an immersion. The *conormal algebra $\mathcal{C}_{Z/X, *}$ of $Z$ in $X$* or the *conormal algebra of $f$* is the quasi-coherent sheaf of graded $\mathcal{O}_ Z$-algebras $\bigoplus _{n \geq 0} \mathcal{I}^ n/\mathcal{I}^{n + 1}$ described above.

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